inconsequentiality of non-Euclidean geometry

non-Euclidean geometry は、 n-sphere を扱うが、 n-sphere 自体がn-次元で二次元では無く、又、Euclid の fifth postulate


If the sum of the interior angles α and β is less than 180°, the two straight lines, produced indefinitely, meet on that side.

If a line segment  intersects two straight lines forming two interior angles on the same side that are less than two right angles , then the two lines, if extended indefinitely, meet on that side on which the angles sum to less than two right angles.




                                     ὅπερ ἔδει δεῖξαι